Finding current using in a loop

[seto6]

NOT ASKING FOR ANSWER JUST EXPLANATION, IM REDOING THIS QUESTION FOR FINALS, I HAD PROBLEM WITH THIS BEFORE, BUT FORGOT TO NOTE DOWN WHY...

Homework Statement

Homework Equations

its given in the problem

The Attempt at a Solution

well i have done this, and was looking over it and not sure why they multiply flux by:dI/dt

can some one clear this up for me
EDIT: is it b/c after doing that we get dI/dt = 100S/s. i think it is, just want to make sure b/c when i did it i use of 100A/s as--> (100A/s)t...t--> time and did it and got correct answer

 

[seto6]

i think i got it can some one make sure

 

[Brown Arrow]

yeah you reasoning is correct. if you use I=100t when you derive you will get 100, which is same as 100A/s.